%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL261-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:01:36 PM UTC 2026
% Result : Unsatisfiable 9.38s 1.78s
% Output : Proof 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f5_nnf,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t3,plain,
or(not(X1),X2) = implies(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t12,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t3]) ).
cnf(f8,axiom,
and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f8_nnf,plain,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t6,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t47,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(step,[status(thm)],[t6,t12]) ).
cnf(t40,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t47]) ).
cnf(f9,negated_conjecture,
~ theorem(or(not(p),or(not(q),and(p,q)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f9_nnf,plain,
~ theorem(or(not(p),or(not(q),and(p,q)))),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ theorem(or(not(p),or(not(q),and(p,q)))),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ theorem(or(not(p),or(not(q),and(p,q)))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(p),or(not(q),and(p,q)))) != true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
theorem(or(not(p),implies(q,and(p,q)))) != true,
inference(rw,[status(thm)],[goal_0,t12]) ).
cnf(g0_1,plain,
theorem(implies(p,implies(q,and(p,q)))) != true,
inference(rw,[status(thm)],[g0_0,t12]) ).
cnf(g0_2,plain,
theorem(implies(p,implies(q,and(p,q)))) != theorem(implies(p,implies(q,not(implies(p,not(q)))))),
inference(rw,[status(thm)],[g0_1]) ).
cnf(g0_3,plain,
theorem(implies(p,implies(q,and(p,q)))) != theorem(implies(p,implies(q,and(p,q)))),
inference(rw,[status(thm)],[g0_2,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL261-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 22:39:33 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.38/1.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.38/1.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------